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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2500.1.b.a $2$ $1.248$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) $-$ \(q-q^{2}+q^{4}-q^{8}+q^{9}+(1-\beta )q^{13}+\cdots\)
2500.1.b.b $2$ $1.248$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) $-$ \(q+q^{2}+q^{4}+q^{8}+q^{9}+(-1+\beta )q^{13}+\cdots\)
2500.1.d.a $4$ $1.248$ \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{3}q^{2}-q^{4}-\beta _{3}q^{8}-q^{9}-\beta _{1}q^{13}+\cdots\)
2500.1.h.a $4$ $1.248$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-5}) \) None \(-1\) \(-2\) \(0\) \(-2\) $-$ \(q+\zeta_{10}^{4}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}-\zeta_{10}^{3}q^{4}+\cdots\)
2500.1.h.b $4$ $1.248$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-5}) \) None \(-1\) \(3\) \(0\) \(-2\) $-$ \(q+\zeta_{10}^{4}q^{2}+(1-\zeta_{10})q^{3}-\zeta_{10}^{3}q^{4}+\cdots\)
2500.1.h.c $4$ $1.248$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-5}) \) None \(1\) \(-3\) \(0\) \(2\) $-$ \(q-\zeta_{10}^{4}q^{2}+(-1+\zeta_{10})q^{3}-\zeta_{10}^{3}q^{4}+\cdots\)
2500.1.h.d $4$ $1.248$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-5}) \) None \(1\) \(2\) \(0\) \(2\) $-$ \(q-\zeta_{10}^{4}q^{2}+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{3}+\cdots\)
2500.1.h.e $8$ $1.248$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{20}^{3}q^{2}+\zeta_{20}^{6}q^{4}+\zeta_{20}^{9}q^{8}+\cdots\)
2500.1.j.a $4$ $1.248$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{8}+\zeta_{10}^{2}q^{9}+\cdots\)
2500.1.j.b $4$ $1.248$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}-\zeta_{10}^{4}q^{8}+\zeta_{10}^{2}q^{9}+\cdots\)
2500.1.j.c $8$ $1.248$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{20}q^{2}+(\zeta_{20}-\zeta_{20}^{3})q^{3}+\zeta_{20}^{2}q^{4}+\cdots\)
2500.1.j.d $8$ $1.248$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{20}q^{2}+(\zeta_{20}^{5}+\zeta_{20}^{9})q^{3}+\zeta_{20}^{2}q^{4}+\cdots\)
2500.1.n.a $40$ $1.248$ \(\Q(\zeta_{100})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{100}q^{2}+\zeta_{100}^{2}q^{4}-\zeta_{100}^{3}q^{8}+\zeta_{100}^{14}q^{9}+\cdots\)
2500.1.p.a $20$ $1.248$ \(\Q(\zeta_{50})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{50}^{3}q^{2}+\zeta_{50}^{6}q^{4}+\zeta_{50}^{9}q^{8}+\cdots\)
2500.1.t.a $100$ $1.248$ \(\Q(\zeta_{250})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{250}^{81}q^{2}-\zeta_{250}^{37}q^{4}+\zeta_{250}^{58}q^{5}+\cdots\)
2500.2.a.a $2$ $19.963$ \(\Q(\sqrt{5}) \) None None \(0\) \(-1\) \(0\) \(1\) $-$ \(q-\beta q^{3}+\beta q^{7}+(-2+\beta )q^{9}+(2+\beta )q^{11}+\cdots\)
2500.2.a.b $2$ $19.963$ \(\Q(\sqrt{5}) \) None None \(0\) \(1\) \(0\) \(-1\) $+$ \(q+\beta q^{3}-\beta q^{7}+(-2+\beta )q^{9}+(2+\beta )q^{11}+\cdots\)
2500.2.a.c $6$ $19.963$ 6.6.103238125.1 None None \(0\) \(-1\) \(0\) \(1\) $-$ \(q-\beta _{1}q^{3}+(1-\beta _{3}+\beta _{4})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
2500.2.a.d $6$ $19.963$ 6.6.103238125.1 None None \(0\) \(1\) \(0\) \(-1\) $-$ \(q+\beta _{1}q^{3}+(-1+\beta _{3}-\beta _{4})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
2500.2.a.e $8$ $19.963$ 8.8.\(\cdots\).1 None None \(0\) \(-5\) \(0\) \(0\) $+$ \(q+(-1+\beta _{1})q^{3}+(-\beta _{2}-\beta _{4}-\beta _{7})q^{7}+\cdots\)
2500.2.a.f $8$ $19.963$ 8.8.\(\cdots\).2 None None \(0\) \(0\) \(0\) \(0\) $+$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{6})q^{7}+\beta _{2}q^{9}+\cdots\)
2500.2.a.g $8$ $19.963$ 8.8.\(\cdots\).1 None None \(0\) \(5\) \(0\) \(0\) $-$ \(q+(1-\beta _{1})q^{3}+(\beta _{2}+\beta _{4}+\beta _{7})q^{7}+(2+\cdots)q^{9}+\cdots\)
2500.2.c.a $4$ $19.963$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{3}+\beta _{1}q^{7}+(2+\beta _{2})q^{9}+(2-\beta _{2}+\cdots)q^{11}+\cdots\)
2500.2.c.b $8$ $19.963$ 8.0.58140625.2 None None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{4}q^{3}+(-\beta _{4}-\beta _{6})q^{7}-\beta _{3}q^{9}+\cdots\)
2500.2.c.c $12$ $19.963$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{3}+\beta _{8}q^{7}+(-2+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots\)
2500.2.c.d $16$ $19.963$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{4}q^{3}-\beta _{15}q^{7}+(-2-\beta _{7})q^{9}+\cdots\)
2500.4.a.a $10$ $147.505$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(-13\) \(0\) \(-8\) $-$ \(q+(-1-\beta _{1})q^{3}+(-2-2\beta _{2}+\beta _{6}+\cdots)q^{7}+\cdots\)
2500.4.a.b $10$ $147.505$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(13\) \(0\) \(8\) $+$ \(q+(1+\beta _{1})q^{3}+(2+2\beta _{2}-\beta _{6})q^{7}+(8+\cdots)q^{9}+\cdots\)
2500.4.a.c $14$ $147.505$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(-2\) \(0\) \(8\) $-$ \(q-\beta _{1}q^{3}+(1-\beta _{2}+\beta _{3})q^{7}+(9+\beta _{1}+\cdots)q^{9}+\cdots\)
2500.4.a.d $14$ $147.505$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(2\) \(0\) \(-8\) $-$ \(q+\beta _{1}q^{3}+(-1+\beta _{2}-\beta _{3})q^{7}+(9+\beta _{1}+\cdots)q^{9}+\cdots\)
2500.4.a.e $20$ $147.505$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(-1\) \(0\) \(-26\) $+$ \(q-\beta _{1}q^{3}+(-2+\beta _{5}-\beta _{6})q^{7}+(9+\beta _{2}+\cdots)q^{9}+\cdots\)
2500.4.a.f $20$ $147.505$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(1\) \(0\) \(26\) $-$ \(q+\beta _{1}q^{3}+(2-\beta _{5}+\beta _{6})q^{7}+(9+\beta _{2}+\cdots)q^{9}+\cdots\)
2500.4.a.g $32$ $147.505$ None None \(0\) \(0\) \(0\) \(0\) $+$
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